Nodal analysis has been used in the petroleum industry to analyze the performance of production systems composed of interacting components. Conventional nodal analysis typically involves selecting a division point and dividing the system at this point. All of the components upstream of the node are referred to as inflow, while those downstream are referred to as outflow. Flow relationships of inflow and outflow are then solved using their respective computation methods, the results of which are usually termed inflow performance relationship (IPR) and outflow performance relationship, both as functions of flowing pressure and rate. The intersection of these two curves gives the nodal solution.
Conventional nodal analysis, however, has been found to lack accuracy. Traditional IPR using Darcy's flow equation assumes a stationary state of the inflow system, that is, constant reservoir pressure. The depletion of a reservoir, when it should be the result of nodal analysis, is merely modeled by the change of reservoir pressure as an input known a priori. The concept of transient IPR was developed to overcome the inadequacy of traditional IPR through the introduction of time as a variable in the model, typically using well test solutions. IPR models have been developed, for example, for radial flow and fracture flow, and by so doing, transient behavior of the inflow system may be modeled. However, it has been found that transient IPR, as a function of reservoir/well parameters and time only, often falls short of acknowledging the production history. Transient IPR is limited to a single time slice, or snap shot, of the whole production life and may assume a pseudo-steady-state. Production history is either excluded altogether from the model or addressed just from a material balance perspective.
In addition, traditional IPR models that are used widely might only be valid if the real reservoir/well model is as simple as assumed. Nodal analysis is generally performed on a well-by-well basis, and in some cases, no interference effect of neighboring well production is considered, not to mention conducting a nodal analysis simultaneously for multiple wells.
For other applications, reservoir simulation has traditionally been used by reservoir engineers to match history and predict performance of underground reservoir systems having multiple wells. However, it has been found that in practice, it takes considerable time and effort to construct reservoir models, and such reservoir models have not been thought to be well suited for use in nodal analysis associated with production operations, particularly due to their reliance on numerical reservoir simulation.
Therefore, a continuing need exists in the art for improved nodal analysis techniques for use in analyzing the performance of nodes in petroleum production systems.